Basic Math Examples

${(x - \frac{1}{5})}^{- 10}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(x - \frac{1}{5})}^{10}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{{(x \cdot \frac{5}{5} - \frac{1}{5})}^{10}}$

Step 2.2

Combine $x$ and $\frac{5}{5}$ .

$\frac{1}{{(\frac{x \cdot 5}{5} - \frac{1}{5})}^{10}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{1}{{(\frac{x \cdot 5 - 1}{5})}^{10}}$

Step 2.4

Move $5$ to the left of $x$ .

$\frac{1}{{(\frac{5 x - 1}{5})}^{10}}$

Step 2.5

Apply the product rule to $\frac{5 x - 1}{5}$ .

$\frac{1}{\frac{{(5 x - 1)}^{10}}{5^{10}}}$

Step 2.6

Raise $5$ to the power of $10$ .

$\frac{1}{\frac{{(5 x - 1)}^{10}}{9765625}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{9765625}{{(5 x - 1)}^{10}}$

Step 4

Multiply $\frac{9765625}{{(5 x - 1)}^{10}}$ by $1$ .

$\frac{9765625}{{(5 x - 1)}^{10}}$